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moo5003

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I'm doing improper integrals for my real analysis class and the problem is stated as:

Calculate a) Integral from 0 to 1 of log(x)

Work: Derivative of (xlog(x)-x) = log(x) thus: let 0<d<1

Lim d-> 0 (from the right) Integral from d to 1 of log(x) = Lim d -> 0 xlog(x)-x evaluated from d to 1 = lim d -> 0 of d-1-dlog(d) = 0 - 1 - 0*-Infinity = -1

Integral from 0 to 1 of Log(x) = -1

Though, when i do this on my calculator i get something around -.43.

Similarly I get:

Integral from 2 to Infinity of Log(x)/x = -log^2(2)/2

Integral from 0 to Infinity of 1/(x^2+1) = Undefined (since Lim x->Infinity of Tan^-1(x) does not exist).

For part b/c. Thanks for anyhelp you can provide in finding my mistake at least for part a so I can recheck part b/c.